logx1/4 = -1 x= 4 log2x^2= 2 x=2 log2x^2=-4 x= 1/4 log125 1/5=x x= -1/3 log1/2 √2=x x= -1/2
Korzystamy z definicji logarytmu: [latex]log_{a}b=c iff a^{c}=b[/latex] a) [latex]log_{x}frac{1}{4}=-1\\x^{-1}=frac{1}{4}\\x^{-1}=4^{-1}\x=4 o log_{4}frac{1}{4}=-1[/latex] b) [latex]log_{2}x^{2}=2\x^{2}=2^{2}\x=2 o log_{2}2^{2}=2[/latex] c) [latex]log_{125}frac{1}{5}=x\\125^{x}=frac{1}{5}\\(5^{3})^{x}=5^{-1}\5^{3x}=5^{-1}\3x=-1 /:3\x=-frac{1}{3} o log_{125}frac{1}{5}=-frac{1}{3}[/latex] d) [latex]log_{frac{1}{2}}sqrt{2}=x\\(frac{1}{2})^{x}=sqrt{2}\\(2^{-1})^{x}=2^frac{1}{2}\\2^{-x}=2^{frac{1}{2}}\\-x=frac{1}{2} /:(-1)\\x=-frac{1}{2} o log_frac{1}{2}}sqrt{2}=-frac{1}{2}[/latex]
